Order 2 Icosahedron Puzzle
I forgot to indicate that
if we put 12 Simplex Stars onto the 12 concaved parts of the Ball-Shaped object formed by 20 octahedrons connected together, then
it will become a larger (order 2) Regular Icosahedron. we can obviously see the larger Regular Icosahedron...
I found a special equation about 29 years ago (with a FORTRAN Program) -
3**3 + 4**3 + 5**3 = 6**3
I was/am not a mathematician, not able to fully understand the meaning behind this equation, maybe someone can derive some useful ideas like Pythagoras' theorem.
Is this equation related to...
Thank Hurkyl.
I have to tell you why I think a regular icosahedron is 20 regular tetrahedrons being put together. There is a long story, I sumarize it as short as possible.
(1). A regular Icosahedron has 20 faces that are equilateral triangles. A regular tetrahedron has 4 faces that are...
I know that a theorem can be deduced from the AXIOMS of a formal system,
but I do not know how to prove an axiom.
Would you please teach me ?
How to prove an axiom ?
How did the axiomatic rules become axiom ?
I think some statements or formulas are axiomatic, although they seem...
Thank Hurkyl again.
I just visited a website having many useful information.
http://www.intent.com/sg/polyhedra.html
There is a Table of Platonic And Archimedean Solids
(Updated: Wed, 26 Mar 2003.)
I got some values as below -
Platonic Icosahedron
total surface area (when edge...
Thank bogdan.
Have you tried to glue 20 regular tetrahedron models to form the regular icosahedron shape ?
I did so, and it is definitely possible.
I found the relationship between s and R (of previous question) is
R = s
or
The circumdiameter of the regular icosahedron is two...
Thank Hurkyl.
But if we pack five Regular Tetrahedron pieces together, surely we can get a Pentagonal-like structure. I do not know its formal name, therefore I just called it Simplex Star.
A Simplex Star formed by 5 regular tetrahedrons, has 7 vertices, 10 faces and 15 edges. Five of the...
Thank marcus.
I am not a mathematician, so I really need the teaching.
I had visited askgeeve.com a few days ago, this site gave me many
formulas of the volumes of Polyhedras, but I could not understand them. I am mostly interested to confirm my assumption -
A Regular Icosahedron can be made...
Please teach me.
Is one Regular Icosahedron equal to twenty Regular Tetrahedrons ?
If the edgelength of both Regular Polyhedras is 1,
What would be their volumes ?
Can we prove (or disprove) the equation below ?
volume of Regular Icosahedron = 20 * volume of Regular Tetrahedron...